A triangle has sides A, B, and C. The angle between sides A and B is pi/3. If side C has a length of 2 and the angle between sides B and C is pi/12, what is the length of side A?

1 Answer
Harish Chandra Rajpoot
Jun 19, 2018

In \Delta ABC, Let \angle A=\frac{\pi}{12}, \angle C=\frac{\pi}{3} & AB=2 as per given data
Now, using sine rule in \Delta ABC as follows
\frac{BC}{\sin\angle A }=\frac{AB}{\sin \angle C}
BC=\frac{AB\sin \angle A}{\sin \angleC}
=\frac{2\sin \frac{\pi}{12}}{\sin \frac{\pi}{3}}
=\frac{2\cdot \frac{\sqrt3-1}{2\sqrt2}}{ \frac{\sqrt3}{2}}
=\frac{\sqrt6-\sqrt2}{\sqrt3}

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